Confidence Intervals

Summary :

This chapter introduces confidence intervals through an everyday example, estimating the average number of candies in a bag, building toward the formal idea of an interval estimate. It covers calculating and interpreting confidence intervals for a population mean and proportion, the Student's t-distribution, and how sample size affects margin of error.

From a point estimate to an interval estimate

Starting from the familiar problem of estimating a mean, such as the mean rent of an apartment or the average number of candies in a bag, the chapter shows that a single point estimate is unlikely to equal the true population value exactly, motivating the construction of a confidence interval, a range of values calculated from sample data that is likely to contain the unknown parameter.

The Student's t-distribution

By the end of the chapter students can discriminate between problems that call for the normal distribution and those that call for the Student's t-distribution, which is used in place of the normal distribution when the population standard deviation is unknown and must be estimated from the sample, with the t-distribution's shape changing as the sample size changes.

Sample size for a target confidence level

The chapter also covers calculating the sample size required to estimate a population mean or proportion for a given desired confidence level and margin of error, giving students a way to plan a study in advance rather than only analyzing data that has already been collected.